Crossover from an incommensurate singlet spiral state with a vanishingly small spin gap to a valence-bond solid state in dimerized frustrated ferromagnetic spin chains

Abstract

Motivated by the magnetic properties of the spin-chain compounds LiCuSbO4≡LiSbCuO4 and Rb2Cu2Mo3O12, we study the ground state of the Heisenberg chain with dimerized nearest-neighbor ferromagnetic (FM) (J1, J 1 < 0) and next-nearest-neighbor antiferromagnetic (J2 > 0) couplings. Using the density-matrix renormalization group technique and spin-wave theory we find a first-order transition between a fully-polarized FM and an incommensurate spiral state at 2α = β/(1 + β), where α is the frustration ratio J2/|J1| and β the degree of dimerization J 1 /J1. In the singlet spiral state the spin-gap is vanishingly small in the vicinity of the FM transition, corresponding to a situation of LiCuSbO4. For larger α, corresponding to Rb2Cu2Mo3O12, and smaller β there is a crossover from this frustration induced incommensurate state to an Affleck-Lieb-Kennedy-Tasaki-type valence bond solid state with substantial spin-gaps. Introduction.-The exotic phenomena emerged by magnetic frustration have long been fascinating subjects of research in condensed matter physics [1]. Nowadays, quasi one-dimensional (1D) frustrated systems, despite their simple structure, are at the center of attention as a playground for novel ground states that can emerge from frustration and strong quantum fluctuations due to low dimensionality. So far, various unconventional magnetic states such as quantum spin liquids [2,3], spin-Peierls states [4], and Tomonaga-Luttinger (TL) liquid phases [5] have been investigated. Currently, among the hottest topics are magnetic multipolar and in particular spin-nematic states [6][7][8][9][10][11] in which magnon bound states are formed from a subtle competition between geometrical balance of ferromagnetic (FM) and antiferromagnetic (AFM) correlations among spins.

Coexistence of valence-bond formation and topological order in the Frustrated Ferromagnetic $J_1$-$J_2$ Chain

“…The saturation value is slightly split depending on whether the system is divided inside or outside the effective S = 1 site. In a VBS state, S L (l) approaches the saturation value S sat L exponentially, i.e., S L (l) ∼ S sat L − a exp(−l/ξ ent ); while, the spin-spin correlation decays with distance exponentially, i.e., | S z 0 S z r | ∼ b exp(−r/ξ corr ) [31]. For the AKLT VBS state ξ ent and ξ corr must coincide, which is indeed what we observe numerically in the D 3 -VBS state.…”

Signatures of a magnetic field-induced unconventional nematic liquid in the frustrated and anisotropic spin-chain cuprate LiCuSbO4

“…Note that the NN exchange integrals may have a margin of error about a few ten K due to several uncertainties like in U eff and a more accurate estimation is left for future work. However, the alternation of the NN exchange integrals is most likely, a rare situation so far only met for the celebrated spin-Peierls compound CuGeO 3 [66] with two AFM NN couplings and probably with two ferromagnetic ones for Rb 2 Cu 2 Mo 3 O 12 [65,67], only. The interchain transfer integrals were derived employing the calculated Wannier functions to reproduce the full DFT band dispersion of the band complex near the Fermi energy.…”

Roles of easy-plane and easy-axis XXZ anisotropy and bond alternation on a frustrated ferromagnetic spin-$1/2$ chain

“…The subscript + or -denotes the relative sign of the xy, and z components of the dimer order parameters and is opposite to the parity eigenvalue of the ground state 39 . The spin gap in this D + phase is orders of magnitude smaller 1,2, 26,31,32 than in another D + phase realized for antiferromagnetic J 1 32,[40][41][42][43][44][45][46] . With increasing easy-plane exchange anisotropy, namely, decreasing ∆ xy from unity, a gapless vector-chiral (VC) phase appears robustly 1 .…”

“…The phase diagram and the spin gap ∆ G in the SU(2)symmetric case (∆ xy = ∆ z ) have been studied in detail 2,26,31,32 : ∆ G is extremely small for δ = 0 and monotonically increases with increasing |δ|, and the first-order phase transition occurs between the TLL and D + phases at…”

“…The model has been studied intensively and extensively in the Heisenberg (∆ xy = ∆ z = 1) 2, [23][24][25][26][27][28][29][30][31][32] and easyplane (∆ xy = 1 and 0 < ∆ z < 1) cases 1,2,24, [33][34][35][36][37][38] . For J 1 /J 2 −4, the ground state belongs to a Tomonaga-Luttinger liquid (TLL) phase with a quasi-long-range ferromagnetic order 24 .…”